[4] LINDGAARD E, LUND E, RASMUSSEN K. Nonlinear buckling optimization of composite structures considering "worst" shape imperfections[J]. International Journal of Solids and Structures, 47, 3186-3202(2010).

[5] WANG B, HAO P, LI G et al. Determination of realistic worst imperfection for cylindrical shells using surrogate model[J]. Structural and Multidisciplinary Optimization, 48, 777-794(2013).

[6] VENKATARAMAN S, LAMBERTI L, HAFTKA R T. Challenges in comparing numerical solutions for optimum weights of stiffened shells[J]. Journal of Spacecraft and Rockets, 40, 183-192(2003).

[8] [8] KAPANIA R K, LI J, KAPO H. Optimal design of unitized panels with curvilinear stiffeners[C]AIAA 5th Aviation Technology, Integration, Operations, 16th LighterThanAir Balloon Systems Conferences. Arlington: AIAA, 2005: 7482.

[9] MULANI S B, SLEMP W C H, KAPANIA R K. EBF3PanelOpt: an optimization framework for curvilinear blade-stiffened panels[J]. Thin-Walled Structures, 63, 13-26(2013).

[10] SLEMP W C H, BIRD R K, KAPANIA R K et al. Design, optimization, and evaluation of integrally stiffened Al-7050 panel with curved stiffeners[J]. Journal of Aircraft, 48, 1163-1175(2011).

[11] WANG D, ABDALLA M M, WANG Z P et al. Streamline stiffener path optimization (SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures[J]. Computer Methods in Applied Mechanics and Engineering, 344, 1021-1050(2019).

[12] HAO P, WANG B, TIAN K et al. Efficient optimization of cylindrical stiffened shells with reinforced cutouts by curvilinear stiffeners[J]. AIAA Journal, 54, 1350-1363(2016).

[13] HAO P, WANG Y T, LIU C et al. Hierarchical nondeterministic optimization of curvilinearly stiffened panel with multicutouts[J]. AIAA Journal, 56, 4180-4194(2018).

[14] LIU D C, HAO P, ZHANG K P et al. On the integrated design of curvilinearly grid-stiffened panel with non-uniform distribution and variable stiffener profile[J]. Materials & Design, 190, 108556(2020).

[15] WANG H D, JIN Y C, JAN J O et al. Data-driven surrogate-assisted multiobjective evolutionary optimization of a trauma system[J]. IEEE Transactions on Evolutionary Computation, 20, 939-952(2016).

[16] [16] EMMERICH M, GIOTIS A, ÖZDEMIR M, et al. Metamodelassisted evolution strategies[C]Parallel Problem Solving From Nature—PPSN ⅤⅡ. Granada: PPSN, 2002: 361–370.

[17] JIN Y C, OLHOFER M, SENDHOFF B. A framework for evolutionary optimization with approximate fitness functions[J]. IEEE Transactions on Evolutionary Computation, 6, 481-494(2002).

[18] JIN Y C, WANG H D, CHUGH T et al. Data-driven evolutionary optimization: an overview and case studies[J]. IEEE Transactions on Evolutionary Computation, 23, 442-458(2019).

[19] FINOL D, LU Y, MAHADEVAN V et al. Deep convolutional neural networks for eigenvalue problems in mechanics[J]. International Journal for Numerical Methods in Engineering, 118, 258-275(2019).

[20] LI X, LIU Z L, CUI S Q et al. Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning[J]. Computer Methods in Applied Mechanics and Engineering, 347, 735-753(2019).

[21] LI X, NING S W, LIU Z L et al. Designing phononic crystal with anticipated band gap through a deep learning based data-driven method[J]. Computer Methods in Applied Mechanics and Engineering, 361, 112737(2020).

[22] SUN L N, GAO H, PAN S W et al. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data[J]. Computer Methods in Applied Mechanics and Engineering, 361, 112732(2020).

[23] YAO H P, GAO Y, LIU Y M. FEA-Net: a physics-guided data-driven model for efficient mechanical response prediction[J]. Computer Methods in Applied Mechanics and Engineering, 363, 112892(2020).

[24] HAO P, LIU D C, ZHANG K P et al. Intelligent layout design of curvilinearly stiffened panels via deep learning-based method[J]. Materials & Design, 197, 109180(2021).

[25] [25] ZHOU Z Z, ONG Y S, NGUYEN M H, et al. A study on polynomial regression Gaussian process global surrogate model in hierarchical surrogateassisted evolutionary algithm[C]2005 IEEE Congress on Evolutionary Computation. Edinburgh: IEEE, 2005: 28322839.

[27] SUN C L, JIN Y C, CHENG R et al. Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems[J]. IEEE Transactions on Evolutionary Computation, 21, 644-660(2017).

[29] [29] MARTÍNEZ S Z, COELLO C A C. MOEAD assisted by RBF wks f expensive multiobjective optimization problems[C]Proceedings of the 15th Annual Conference on Geic Evolutionary Computation. New Yk: GECCO, 2013: 1405–1412.

[30] CESA-BIANCHI N, CONCONI A, GENTILE C. On the generalization ability of on-line learning algorithms[J]. IEEE Transactions on Information Theory, 50, 2050-2057(2004).

[31] [31] GOODFELLOW I, BENGIO Y, COURVILLE A. Deep learning[M]. Cambridge: The MIT Press, 2016: 201–226.

[32] [32] BOUREAU Y L, PONCE J, LECUN Y. A theetical analysis of feature pooling in visual recognition[C]Proceedings of the 27th International Conference on Machine Learning (ICML10). Haifa, Israel: ICML, 2010.

[33] [33] WANG T, WU D J, COATES A, et al. Endtoend text recognition with convolutional neural wks[C]Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012). Tsukuba: IEEE, 2012: 3304–3308.

[34] [34] WIJNHOVEN R G J, DE WITH P H N. Fast training of object detection using stochastic gradient descent[C]2010 20th International Conference on Pattern Recognition. Istanbul,Turkey: IEEE, 2010: 424–427.

[35] [35] ALPAYDIN E. Introduction to machine learning[M]. 4th ed. Cambridge: The MIT Press, 2020.

[36] [36] ZHANG H H, ZHANG K S. Surrogatebased optimization[M]RealWld Applications of Geic Algithms. London: Imperial College Press, 2012: 343–362.

[37] MCDONALD K, LITTLE J, PEARCY M et al. Development of a multi-scale finite element model of the osteoporotic lumbar vertebral body for the investigation of apparent level vertebra mechanics and micro-level trabecular mechanics[J]. Medical Engineering & Physics, 32, 653-661(2010).

[38] HYNDMAN R J, KOEHLER A B. Another look at measures of forecast accuracy[J]. International Journal of Forecast, 22, 679-688(2006).

[39] [39] WANG J, LIU S C, LI M C, et al. Multiobjective geic algithm strategies f burnable poison design of pressurized water react[JOL]. International Journal of Energy Research. (20200906). https:onlinelibrary.wiley.comdoiepdf10.1002er.5926.